A rooted-forest partition with uniform vertex demand

Naoki Katoh () and Shin-ichi Tanigawa ()
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Naoki Katoh: Kyoto University
Shin-ichi Tanigawa: Kyoto University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 2, No 2, 67-98

Abstract: Abstract A rooted-forest is the union of vertex-disjoint rooted-trees. Suppose we are given a graph G=(V,E), a collection {R 1,…,R k } of k root-sets (i.e., vertex-sets), and a positive integer d. We prove a necessary and sufficient condition for G to contain k edge-disjoint rooted-forests F 1,…,F k with root-sets R 1,…,R k such that each vertex is spanned by exactly d of F 1,…,F k .

Keywords: Rooted-forest partition; Tree-packing; Matroids (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-010-9367-x

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